This paper surveys some recent theoretical results on the efficiency of machine learning algorithms. The main tool described is the notion of Probably Approximately Correct (PAC) 1 earning, introduced by Valiant. We define this learning model and then look at sorne of the results obtained in it. We then consider some criticisms of the PAC model and the extensions proposed to address these criti...

While Myerson’s theorem provides an elegant solution to the optimal auction design problem for k-good auctions, his auction is rather complicated, and is consequently not widely used in practice. On the other hand, posted-price mechanisms are widely used in practice. We have derived an optimal posted-price mechanism for an auction with a single bidder.1 What about for multiple bidders? What is ...

Learning quickly when irrelevant attributes abound: a new linear-threshold algorithm. of empirical and explanation-based learning algo

Article history: Received 8 July 2013 Received in revised form 25 May 2014 Accepted 30 May 2014 Available online 4 June 2014 Communicated by Amit Singer

We consider the problem of searching a document collection using a set of independent computers. That is, the computers do not cooperate with one another either (i) to acquire their local index of documents or (ii) during the retrieval of a document. During the acquisition phase, each computer is assumed to randomly sample a subset of the entire collection. During retrieval, the query is issued...

We show that auctions can generate near optimal total expected revenue by not using optimal reserve prices. Suppose we have n = 1 bidders in a posted-price, sealed-bid auction. This bidder has type v i drawn from distribution F. We can describe what the expected revenue is with a functionˆR : T → R: ˆ R(p) = p(1 − F(p)). (1) Figures 1 and 2 show expected revenue functions for the exponential di...

Unification with constants modulo the theory ACUI of an associative (A), commutative (C) and idempotent (I) binary function symbol with a unit (U) corresponds to solving a very simple type of set equations. It is well-known that solvability of systems of such equations can be decided in polynomial time by reducing it to satisfiability of propositional Horn formulae. Here we introduce a modified...

Given a string w and a pattern p, approximate pattern matching merges traditional sequence comparison and pattern matching by asking for the minimum diierence between w and a string exactly matched by p. We give an O(PN 2 (N + logP)) algorithm for approximately matching a string of length N and a context-free language speciied by a grammar of size P. The algorithm generalizes the Cocke-Younger-...

We present a very simple, randomized approximation algorithm for determining the number of cliques in a random graph. Supported in part by NSF Grant CCR-9505448 and a UC Berkeley Faculty Research Grant

We propose and investigate from the algorithmic standpoint a novel form of fuzzy query called approximately dominating representatives or ADRs. The ADRs of a multidimensional point set consist of a few points guaranteed to contain an approximate optimum of any monotone Lipschitz continuous combining function of the dimensions. ADRs can be computed by appropriately post-processing Pareto, or “sk...